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A jacket lists for $200. At Store P the clerk first takes x percent off the list price and then takes a flat $30 off the reduced price, and the final price is exactly $120. Store Q sells the same jacket by taking the same flat $30 off the list price first and then taking the same x percent off the reduced amount. What is the final price, in dollars, of the jacket at Store Q?
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Correct answer
C
First find x using Store P's order: the percent comes off first, then the flat $30 comes off the reduced price. So 200 × (1 − x/100) − 30 = 120, which gives 200 × (1 − x/100) = 150. Dividing by 200, 1 − x/100 = 0.75, so x/100 = 0.25 and x = 25. The percent discount is 25%, which leaves 75%, that is a multiplier of 0.75, of whatever base it is applied to.
Now apply Store Q's order, where the flat $30 comes off the list price first. Take $30 off $200: 200 − 30 = 170. Then take 25% off the reduced $170: 170 × 0.75 = 127.50. So the final price at Store Q is $127.50, choice C.
A flat-dollar discount and a percent discount do not commute, because the percent acts on a different base depending on the order. At Store P the 25% is taken on the full $200, so it never touches the $30. At Store Q the $30 is removed first, so the 25% is taken on a base that is already $30 smaller. That difference is exactly 25% of $30, which is $7.50, so Store Q's price is $7.50 more than Store P's: 120 + 7.50 = 127.50.
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